NIH funded trial to determine the best and safest way to reduce stroke risk in atrial fibrillation. Based on data from SPAF2, patients with chronic atrial fibrillation will be stratified according to high or low risk of stroke. Patients at low risk will be treated with one aspirin per day (325 mg) and those at high risk of stroke will be randomized to receive either warfarin in a standard dose to maintain a inr at 2-3 or low warfarin (1-3 MG sufficient to mildly elevate the INR to 1.3). Subjects will be followed at regular intervals with baseline and regular neurological examinations to determine and evidence of stroke and to determine any complications of therapy.